Related papers: Blocks and modules for Whittaker pairs

Over an algebraically closed fields, an alternative to the method due to Kostrikin and Shafarevich was recently suggested. It produces all known simple finite dimensional Lie algebras in characteristic p>2. For p=2, we investigate one of…

In this paper we aim to understand the category of stable-Yetter-Drinfeld modules over enveloping algebra of Lie algebras. To do so, we need to define such modules over Lie algebras. These two categories are shown to be isomorphic. A mixed…

Let $A_n=\mathbb{C}[t_i^{\pm1},~1\leq i\leq n]$ and $\mathbf{W}(n)_\mu=A_nd_\mu$ the solenoidal Lie algebra introduced by Y.Billig and V.Futorny in \cite{BiFu2}, where $\mu=(\mu_1,\ldots,\mu_n)\in\mathbb{C}^n$ is a generic vector and…

We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian…

We prove that applying a projective functor to a holonomic simple module over a semi-simple finite dimensional complex Lie algebra produces a module that has an essential semi-simple submodule of finite length. This implies that holonomic…

As a sequel to [Duan-Shu-Yao], we introduce here a category $\mathscr{LC}$ arising from the BGG category $\mathcal{O}$ defined in [Duan-Shu-Yao] for Lie algebras of polynomial vector fields. The objects of $\mathscr{LC}$ are so-called…

A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…

We study weight modules of the Lie algebra $W_2$ of vector fields on ${\mathbb C}^2$. A classification of all simple weight modules of $W_2$ with a uniformly bounded set of weight multiplicities is provided. To achieve this classification…

In this paper, we construct a new class of modules for the Schr\"{o}dinger algebra $\mS$, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schr\"{o}dinger…

In this paper, Lie bialgebra structures on generalized Heisenberg-Virasoro algebra $\mathfrak{L}$ are considered. Also, $H^1({\mathfrak{L}} ,\mathfrak{L}\bigotimes\mathfrak{L})$ is given explicitly. Moreover, it is proved that all Lie…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

We construct common triangular bases for almost all the known (quantum) cluster algebras from Lie theory. These bases provide analogs of the dual canonical bases, long anticipated in cluster theory. In cases where the generalized Cartan…

In this paper, we explore natural connections among trigonometric Lie algebras, (general) affine Lie algebras, and vertex algebras. Among the main results, we obtain a realization of trigonometric Lie algebras as what were called the…

We consider a class of infinite-dimensional, modular, graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series. We identify two subclasses of Nottingham Lie…

This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In…

In this paper, we consider the twisted Hamiltonian extended affine Lie algebra (THEALA). We classify the irreducible integrable modules for these Lie algebras with finite-dimensional weight spaces when the finite-dimensional center acts…

The aim of this paper is to study a Lie conformal algebra of Block type. In this paper, conformal derivation, conformal module of rank 1 and low-dimensional comohology of the Lie conformal algebra of Block type are studied. Also, the vertex…

We derive a formula for the the modular class of a Lie algebroid with a regular twisted Poisson structure in terms of a canonical Lie algebroid representation of the image of the Poisson map. We use this formula to compute the modular…

We construct four new series of generalized simple Lie algebras of Cartan type, using the mixtures of grading operators and down-grading operators. Our results in this paper are further generalizations of those in Osborn's work ``New simple…

In this work, we refine recent results on the explicit construction of polynomial algebras associated with commutants of subalgebras in enveloping algebras of Lie algebras by considering an additional grading with respect to the subalgebra.…